TLmom {lmomco} | R Documentation

## A Sample Trimmed L-moment

### Description

A sample trimmed L-moment (TL-moment) is computed for a vector. The r >= 1 order of the L-moment is specified as well as the level of symmetrical trimming. A trimmed TL-moment is

hat{λ}^{(t)}_r = frac{1}{r}sum^{n-t}_{i=t+1} <=ft[ frac{sumlimits^{r-1}_{k=0}{ (-1)^k {r-1 choose k} {i-1 choose r+t-1-k} {n-i choose t+k} }}{{n choose r+2t}} right] x_{i:n} mbox{,}

where t represents the trimming level of the t-largest or t-smallest values, r represents the order of the L-moments, n represents the sample size, and x_{i:n} represents the ith sample order statistic (x_{1:n} <= x_{2:n} <= ... <= x_{n:n}).

### Usage

    TLmom(x,order,trim=NULL,leftrim=NULL,rightrim=NULL,sortdata)

### Arguments

`x` | A vector of data values.
`order` | L-moment order to use in the computations. Default is 1 (the mean).
`trim` | Level of symmetrical trimming to use in the computations. Although `NULL` in the argument list, the default is 0—the usual L-moment is returned.
`leftrim` | Level of trimming of the left-tail of the sample.
`rightrim` | Level of trimming of the right-tail of the sample.
`sortdata` | A logical switch on whether the data should be sorted. The default is TRUE.

### Value

An R `list` is returned.

`lambda` | The TL-moment of order=`order` and trimming=`trim`.
`order` | L-moment order computed. Default is 1 (the mean).
`trim` | Level of symmetrical trimming used in the computation, which will equal `NULL` if asymmetrical trimming was used.
`leftrim` | Level of left-tail trimming used in the computation.
`rightrim` | Level of right-tail trimming used in the computation.

### Note

The presence of the `sortdata` switch can be dangerous. L-moment computation requires that the data be sorted into the “order statistics”. Thus the default behavior of `sortdata=TRUE` is required when the function is called on its own. In practice, this function would not be used as multiple trimmed L-moments would be needed. Multiple trimmed L-moments are best computed by `TLmoms`, which calls `TLmom` multiple times. The function `TLmoms` takes over the sort operation on the data and passes `sortdata=FALSE` to `TLmom` for efficiency. (The point of this discussion is that one does not want to waste CPU time sorting the data more than once.)

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational statistics and data analysis, vol. 43, pp. 299-314.

### See Also

`TLmoms`

### Examples

    X1 <- rcauchy(30)
    TL <- TLmom(X1,order=2,trim=1)

[Package lmomco version 0.92 Index]